In sensor based planning exploration is unavoidable. To understand this aspect of sensor based planning, the authors consider the problem of motion planning for a point with tactile sensors . In dimensions greater than two, this problem has been shown to be unsolvable given a certain mathematical framework. But, if the formulation of the problem is changed by taking the C-space to be discrete, then path planning with tactile sensors is possible. In this setting we give a resolution complete algorithm for planning the motion of a point in any dimension. Measuring the complexity of the problem by the number of discrete moves that the robot makes, we give an upper bound for the complexity of our algorithm that is linear in the surface area of the boundary of the C-space obstacles
